The uncertainty in the position of features of a fluid (e.g. vortices and fronts) is ubiquitous in geophysical fluid dynamics. This talk will begin by exploring the structure of distributions arising from the uncertainty in the location of a flow feature. It will be shown that the probability density functions associated with these distributions have surprisingly complex, non-Gaussian characteristics. Data assimilation, which is the act of combining information from observations with model forecasts to obtain a state estimate, will be shown to be highly sensitive to the shape of these distributions. It will be argued that the lowest-order effect that should be accounted for in these situations will be the skewness (third moment) of the probability density function. A simple modification to an Ensemble Kalman Filter will be described that adds the capability to use the skewness in the calculation of the state estimate. Along the way I will describe a few contemporary data assimilation algorithms commonly used in the geosciences (i.e. state vectors of 107 to 108 elements).